Question

1) Determine o valor de x:
) = √2 2
) = −√3
)2∗= −1,
) 1 + = 0,
) = √2
)= √2
0<<2 − < <

Answer 1

Explicação passo-a-passo:

Z

2x(x

2 + 3)2

dx

11- Z

1 + 4x

√

1 + x + 2x

2

dx

19- Z

sin(πt) dt

21- Z

(ln x)

2

x

dx

31- Z

1

x ln x

dx

Respostas: 7. f(x) = 1

5

(x

2 + 3)5 + C, 11. f(x) = 2√

1 + x + 2x

2 + C, 19. f(x) = −

1

π

cos π t + C,

21. f(x) = 1

3

(ln x)

3 + C, 31. f(x) = ln | ln x| + C.

Calcule a integral definida, se ela existir:

53- Z π

0

sec2

(t/4) dt

59- Z π

3

0

sen θ

cos2θ

dθ

Respostas: 53. 4; 59. 1.

Se¸c˜ao 7.1- Integra¸c˜ao por Partes, p´ag. 476: 5, 9, 13, 27, 33 e 35.

Avalie a Integral:

5- Z

re

r

2 dr